The present invention relates to a multi-carrier communication system and a receiver thereof, and more particularly to a multi-carrier communication system using the interference between a target sub-channel and two or more upper and lower sub-channels (ICI) and a receiver thereof.
The bit error rate (BER) of the multi-carrier communication system in filter bank modulation, DMT modulation and FMT modulation can be improved by using receive signals that include distortion by inter-channel interference (ICI). Inter-channel interference occurs by the malfunction of a system in communication systems, such as OFDM-CDMA, or due to an unavoidable environment such as the loss of orthogonality between sub-channels. Inter-channel interference, which is called the “leak of spectrum energy”, at times the cross-talk between sub-channels, is caused by a leak.
A major advantage of the turbo receiver of the present invention is that the phenomenon of ICI is handled as a zero mean Gaussian distribution random variable (e.g. Gaussian approximation used in the following document 1 below), for which a finite state discrete Markov process model is used. For such an ICI model, simple Gaussian approximation seems to be more practical because of the nature of ICI. The turbo receiver of the present invention is based on a maximum posterior probability estimation algorithm. In this turbo receiver, information derived from one sub-channel after non-linear processing refines the estimated maximum posterior probability of the latter channel, and in the same way, the information derived from the other sub-channel refines the estimated maximum probability of the former sub-channel.
Document 1: K. Sathanathan and C. Tellambura: “Probability of error calculation of OFDM system with frequency offset”, IEEE Trans. Commun., Vol. 49, NO. 11, November 2001, pp. 1884-1888.
(a) Relationship Between Frequency Offset and ICI
In the case of a multi-carrier communication system where a band is divided into a plurality of sub-bands, which are independent narrow bands, and the transmission data of each sub-band is frequency-multiplexed and transmitted and received, the selection of a filter set in a multi-carrier communication system for filter bank modulation, DMT (Discrete Multi-tone) modulation and FMT (Filtered Multi-tone) modulation, has been executed under the constraint that inter-symbol interference (ISI) and inter-channel interference (ICI) are completely removed.
In an ideal transmission channel where there is no Doppler shift and where there is no offset frequency between transmitter/receiver and signal distortion does not occur, this constraint guarantees the receiver that the recovery of transmission symbols to be error free. However the frequency offset which is generated in each channel, due to inaccurate tuning of the oscillator and the Doppler shift, causes BER deterioration due to a spectrum leak or ICI.
The only method to relax such deterioration of BER is to minimize the frequency offset, and more particularly, to maintain it to be within 1% of the sub-carrier frequency interval. This method, however, requires accurate frequency offset estimation, and also if the noise level is high when multi-carrier signals mixed with noise are received, the accuracy of frequency offset estimation is affected. Also according to this method, the Doppler shift is not consistent with respect to the transmission symbols in a high-speed fading channel, and operation becomes inaccurate in a high-speed fading channel which changes depending on the time.
Here the case of a DMT base system and an ideal white Gaussian noise (AWGN) channel is assumed. It is also assumed that the level of inter-symbol interference ISI can be ignored compared with the inter-channel interference ICI and other noise signals. To simplify description, only a target channel, the first adjacent sub-channel located below the target sub-channel and the second adjacent sub-channel located above the target sub-channel, are considered. FIG. 1 and FIG. 2 show the frequency response of the three channels in the case when the frequency offset is zero (FIG. 1), and in the case when the frequency offset is not zero (FIG. 2). The signals of the central frequencies f1, f2 and f3 corresponding to the first, second and third sub-channels are indicated by the vertical arrows in FIG. 1 and FIG. 2. In FIG. 1 and FIG. 2, the sub-channel number 0 (ch0) indicates the target sub-channel, the sub-channel number −1 (ch−1) is a sub-channel located below the target sub-channel in the frequency scale, and the sub-channel number +1 (ch+1) indicates the sub-channel located above the target sub-channel in the frequency scale. If the cycle of the DMT symbol is T, then the frequency scale is normalized with a channel interval equal to 1/T. In other words, one unit of the frequency scale is the channel interval. As FIG. 1 shows, when the frequency offset (normalized by the channel interval) α is 0, the transfer function of the lower sub-channel and the upper sub-channel, indicated by the solid line A and the dotted line B in FIG. 1, gives infinite attenuation in the central frequency f2 of the target sub-channel (dotted line C). In the same way, the transfer function of the target sub-channel gives infinite attenuation in the central frequencies f1 and f3 of the lower and the upper sub-channels. In other words, if the frequency offset α is zero, ICI is not generated between adjacent sub-channels. This means that if the frequency offset is zero, the respective sub-channels intersect orthogonally, and ICI does not exist at all.
If the frequency offset α is not zero, however, the orthogonality of the sub-channels is affected, and ICI is generated. FIG. 2 shows the spectrum characteristics of each sub-channel of the DMT system when the frequency offset α is not zero. The spectrum of adjacent channels cross at −3 dB, and the first side-lobe is −13 dB, which is high. In order to avoid a complex system model, the case when the sub-channels which are distant for a 1 or 2 channel interval interfere with each other will be considered below. It is clear that the spectrum of an adjacent sub-channel has a mutual gain which is not zero, which is indicated as α0-1, α1-1, α10, α−10, α01 and α−11. In these notations the first index of a indicates the interference source sub-channel, and the second index indicates the interference target sub-channel. In other words, α−10 indicates the leak transfer coefficient (amplitude) from the lower sub-channel with the sub-channel number −1 to the target channel with the sub-channel number 0. α−11 indicates the leak transfer coefficient (amplitude) from the lower sub-channel with the sub-channel number −1 to the upper sub-channel with the sub-channel number 1, α01 indicates the leak transfer coefficient from the target sub-channel with the sub-channel number 0 to the higher sub-channel with the sub-channel number 1, α0-1 indicates the leak transfer coefficient from the target sub-channel with the sub-channel number 0 to the lower sub-channel with the sub-channel number −1, and α10, indicates the leak transfer coefficient from the higher sub-channel with the sub-channel number +1 to the target sub-channel with the sub-channel number 0. As described above, if the frequency offset α is not zero, the mutual gain which is not zero, that is ICI (cross-talk), is generated between sub-channels.
(b) General Model of Communication System
FIG. 3 is a general model (four sub-channel model) depicting the mutual ICI of four sub-channels in a DMT system having frequency offset. Compared with the three sub-channel model (see FIG. 4), according to the turbo receiver of the present invention, the four sub-channel model can improve the total system BER in more cases because of the low roll off spectrum characteristics of DMT. 11, 12, 13 and 14 are the transmitters of the sub-channels ch−1, ch0, ch+1 and ch+2, 21, 22, 23 and 24 are the receivers of each sub-channel, 31, 32, 33 and 34 are the transmission lines of each sub-channel. 4ij is a multiplier to multiply the sub-channel signal Di by the leak transfer coefficient (interference coefficient) αij of the sub-channel with the number i to the sub-channel with the number j respectively, 51, 52, 53 and 54 are the first synthesizing units for synthesizing the cross-talk (ICI) from the adjacent sub-channel to its own sub-channel signal, 61, 62, 63 and 64 are the second synthesizing units for synthesizing the cross-talk (ICI) from the sub-channel which is distant from two channel intervals to its own sub-channel signal, and 71, 72, 73 and 74 are the noise synthesizing units.
As FIG. 3 shows, the signals from the lower sub-channel ch−1 leak into the target sub-channel ch0 via the cross-talk coefficient α−10, the signals from the upper sub-channel ch+1 leak into the target sub-channel via the cross-talk coefficient α10, and the signals from the upper sub-channel ch+2 leak into the target sub-channel ch0 via the cross-talk coefficient α20. Also the signals from the lower sub-channel ch−2 leak into the target sub-channel via the cross-talk coefficient α−20, but description thereof will be omitted since this can be regarded as the same as the leak from the ch+2. In the model in FIG. 3, the sub-channels that cause mutual interference are limited to the upper and lower sub-channels, but the number of sub-channels in the entire communication system is not limited, so the model in FIG. 3 can also be applied to a multi-carrier communication system that has N number of sub-channels, where N is 4 or a greater number. In such a case as well, interference to each sub-channel is only from the lower two sub-channels and the upper two sub-channels. In this case, the interference coefficient indicates a chain of coefficients. The noise components denoted as n1(t), n2(t), n3(t) and n4(t) in FIG. 3 are statistically independent (no correlation) because of the frequency orthogonality between the sub-channels.
The sub-channels are located in the frequency domain, but this model can be applied not only to a DMT modulation type or a filter bank modulation type system, but also to other systems. The dimensions can be expanded to other domains, such as space (space division multiplex axis) and polarity.
(c) Technical Problem
The model in FIG. 3 is beneficial in terms of understanding the physical process which causes ICI. The problem of this model lies in accurately deciding the receive signals of each sub-channel and the value of the transmission information symbols (a sign if a binary number).
One possible method to reduce ICI in a receiver is applying the decision feedback equalizer (DFE) to cancel ICI, which is proposed in the following document 2.
Document 2: Viterbo and K. Fazel, “How to combat long echoes in QFDM transmission schemes: Sub-channel equalization or more powerful channel coding,” Proc. IEEE Globecom '95, Singapore, November 1995, pp. 2069-2074.
If the output of an individual receiver is in hard bit decision (hard decision) format, then sharing information among sub-channels has only a few benefits. This restricts the operation range of DFE which uses a hard decision.
The above mentioned approach is effective in many practical cases, but is for minimizing the effect of ICI, and is the second best approach. Since ICI includes information on transmission symbols, it is possible to remodulate the receive signals quite well by using this transmission symbol information included in ICI.